A hybrid method to study flow-induced deformation of three-dimensional capsules

A hybrid method is proposed to study the transient deformation of liquid filled capsules with elastic membranes under flow. In this method, the immersed boundary concept is introduced into the framework of lattice Boltzmann method, and the multi-block strategy is employed to refine the mesh near the capsule to increase the accuracy and efficiency of computation. A finite element model is incorporated to obtain the forces acting on the membrane nodes of the three-dimensional capsule which is discretized into flat triangular elements. The present method was validated by studying the transient deformation of initially spherical and oblate-spheroidal capsules with various membrane constitutive laws under shear flow; and there were good agreements with previous theory or numerical results. The versatility of the present method was demonstrated by studying the effects of inertia on the deformation of capsules in shear flow; and the inertia effects were found to be significant. The transient deformation of capsules with initially biconcave discoid shape in shear flow was also studied. The unsteady tank-treading motion was observed, in which the capsule undergoes periodic shape deformation and inclination oscillation while its membrane is rotating around the liquid inside. To our knowledge, this motion of three-dimensional biconcave discoid capsules has not been fully recovered by numerical simulation so far.